Chapter 7, Problem 84RE

a.

To determine

The graph of supply and demand.

Explanation of Solution

Given:

Equation of demand and supply is given as;

  $\begin{array}{l}p=130-0.0002x\mathrm{...1}\\ p=30+0.0003x\mathrm{....2}\end{array}$

To find the equilibrium point equating both demand and supply.

  $130-0.0002x=30+0.0003x$

Now adding $0.002x-30$ in both side.

  $\begin{array}{l}130+0.003x+0.0002x-30=130-0.0002x+0.0002x-30\\ 0.0005x=100\\ x=200000\end{array}$

Now putting the value of x in equation 1.

  $\begin{array}{l}p=130-0.0002\times 200000\\ =130-40\\ =90\end{array}$

Therefore equilibrium point will be $\left(x,p\right)=\left(200000,90\right)$

Now the graph of the supply and demand is shown in below figure.

  

b.

To determine

The consumer surplus and producer surplus.

Answer to Problem 84RE

The consumer surplus is $4000000 and producer surplus is $6000000.

Explanation of Solution

Given:

Equation of demand and supply is given as;

  $\begin{array}{l}p=130-0.0002x\mathrm{...1}\\ p=30+0.0003x\mathrm{....2}\end{array}$

Consumer surplus will be equal to area of below region in the graph.

  $\begin{array}{l}p=130-0.0002x\\ p\ge 90\\ x\ge 0\end{array}$

Therefore consumer surplus is ,

  $\begin{array}{l}\frac{1}{2}bh=\frac{1}{2}\times 200000\times 40\\ =4000000\end{array}$

Producer surplus is equal to area of the bellow region.

  $\begin{array}{l}p=30+0.0003x\\ p\le 90\\ x\ge 0\end{array}$

Therefore producer surplus is ,

  $\begin{array}{l}\frac{1}{2}bh=\frac{1}{2}\times 200000\times 60\\ =6000000\end{array}$

So, the consumer surplus is $4000000 and producer surplus is $6000000.